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// while (clock()<=69*CLOCKS_PER_SEC)
// #pragma comment(linker, "/stack:200000000")
// #pragma GCC optimize("O3")
// #pragma GCC target ("avx2")
// #pragma GCC optimize("Ofast")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
// #pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace __gnu_pbds;
using namespace std;

template <typename T>
using ordered_set =
    tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

#define sim template <class c
#define ris return *this
#define dor > debug &operator<<
#define eni(x)                                                                    \
    sim > typename enable_if<sizeof dud<c>(0) x 1, debug &>::type operator<<(c i) \
    {
sim > struct rge {
    c b, e;
};
sim > rge<c> range(c i, c j) { return rge<c>{i, j}; }
sim > auto dud(c *x) -> decltype(cerr << *x, 0);
sim > char dud(...);
struct debug {
#ifdef XOX
    ~debug()
    {
        cerr << endl;
    }
    eni(!=) cerr << boolalpha << i;
    ris;
} eni(==) ris << range(begin(i), end(i));
}
sim, class b dor(pair<b, c> d)
{
    ris << "" << d.first << " --> " << d.second << "";
}
sim dor(rge<c> d)
{
    *this << "[";
    for (auto it = d.b; it != d.e; ++it)
        *this << ", " + 2 * (it == d.b) << *it;
    ris << "]";
}
#else
    sim dor(const c &)
    {
        ris;
    }
#endif
}
;
#define imie(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "

#ifdef XOX
#warning Times may differ!!!
#endif

#define endl '\n'
#define pb emplace_back
#define vt vector
#define rep(i, a, b) for (int i = a; i < (b); ++i)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;

const int nax = 1e6, mod = 1e9 + 7;

void test_case()
{
    int n;
    string s;
    cin >> n >> s;
    vector<pii> one, two;
    auto make = [&]() {
        auto add = [&](int a, int b) {
            if (a > 0 && s[a - 1] == '1' && b + 1 < n && s[b + 1] == '1')
                two.pb(a, b);
            else
                one.pb(a, b);
        };
        int j = 0;
        for (int i = 0; i < n; i++) {
            if (s[i] != '0') {
                if (j < i) add(j, i - 1);
                j = i + 1;
            }
        }
        if (j < n) add(j, n - 1);
    };
    make();
    sort(all(one), [](const pii &a, const pii &b) { return a.second - a.first > b.second - b.first; });
    sort(all(two), [](const pii &a, const pii &b) { return a.second - a.first > b.second - b.first; });
    debug() << imie(one) imie(two);
    int ans = 0;
    {
        int my_ans = 0;
        int ile_minelo = 0;
        for (auto [l, r] : two) {
            int len = r - l + 1 - 2 * ile_minelo;
            if (len <= 0) break;
            if (len == 1 || len == 2) {
                ile_minelo++;
                my_ans++;
            } else {
                ile_minelo += 2;
                my_ans += len - 1;
            }
        }
        for (auto [l, r] : one) {
            int len = r - l + 1 - ile_minelo;
            if (len <= 0) break;
            ile_minelo++;
            my_ans += len;
        }
        ans = max(ans, my_ans);
    }
    {
        if (size(one) == 2) {
            int my_ans = 0;
            int ile_minelo = 0;
            auto [l1, r1] = one[0];
            auto [l2, r2] = one[1];
            {
                int len = r1 - l1 + 1;
                ile_minelo++;
                my_ans += len;
            }
            for (auto [l, r] : two) {
                int len = r - l + 1 - 2 * ile_minelo;
                if (len <= 0) break;
                if (len == 1 || len == 2) {
                    ile_minelo++;
                    my_ans++;
                } else {
                    ile_minelo += 2;
                    my_ans += len - 1;
                }
            }
            {
                int len = r2 - l2 + 1 - ile_minelo;
                if (len > 0) my_ans += len;
            }
            ans = max(ans, my_ans);
        }
    }
    {
        int my_ans = 0;
        int ile_minelo = 0;
        for (auto [l, r] : one) {
            int len = r - l + 1 - ile_minelo;
            if (len <= 0) break;
            ile_minelo++;
            my_ans += len;
        }
        for (auto [l, r] : two) {
            int len = r - l + 1 - 2 * ile_minelo;
            if (len <= 0) break;
            if (len == 1 || len == 2) {
                ile_minelo++;
                my_ans++;
            } else {
                ile_minelo += 2;
                my_ans += len - 1;
            }
        }
        ans = max(ans, my_ans);
    }
    cout << n - ans << '\n';
}

int main()
{
    cin.tie(nullptr)->sync_with_stdio(0);
    int t;
    cin >> t;
    while (t--)
        test_case();
}